A348368 Numbers k such that w(k + w(k)) < w(k), where w(k) is the binary weight of k, A000120(k).

6, 7, 13, 14, 15, 21, 29, 30, 31, 37, 45, 46, 47, 55, 59, 60, 61, 62, 63, 69, 77, 78, 79, 87, 91, 92, 93, 94, 95, 103, 107, 108, 109, 111, 115, 123, 124, 125, 126, 127, 133, 141, 142, 143, 151, 155, 156, 157, 158, 159, 167, 171, 172, 173, 175, 179, 187, 188, 189

Offset: 1

Author

Ctibor O. Zizka, Oct 15 2021

Keywords

• nonn
• base
• easy

Examples

			k = 91; A000120(91 + A000120(91)) < A000120(91), thus k = 91 is a term.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000120, A092391, A348367.

Programs

Maple

q:= n-> (wt-> is(wt(n+wt(n)) add(i, i=Bits[Split](k))):
select(q, [$0..200])[];  # Alois P. Heinz, Oct 15 2021

Mathematica

h[n_] := DigitCount[n, 2, 1]; q[n_] := h[n + (hn = h[n])] < hn; Select[Range[200], q] (* Amiram Eldar, Oct 15 2021 *)

Python

def h(n): return bin(n).count('1')
def ok(n): return h(n + h(n)) < h(n)
print(list(filter(ok, range(1, 190)))) # Michael S. Branicky, Oct 15 2021

Formula

k : A000120(A092391(k)) < A000120(k); A348367(k) < A000120(k).